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KEAM 2019 Math Paper
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© examsnet.com
Question : 2
Total: 121
If
|
a
|
=
|
b
|
=
|
a
−
b
|
=
1
. Then angle between a and
b
is
π
6
π
4
π
3
π
2
π
8
Validate
Solution:
We know that
|
a
−
b
|
2
=
(
a
−
b
)
⋅
(
a
−
b
)
⇒
(
1
)
2
=
|
a
|
2
+
|
b
|
2
−
2
a
⋅
b
[
∵
|
a
|
−
|
b
|
=
1
]
⇒
1
=
1
+
1
−
2
|
a
|
|
b
|
cos
θ
[
∵
|
a
|
=
|
b
|
=
1
and
θ
is angle between a and
b
]
⇒
1
=
2
−
2
cos
θ
⇒
cos
θ
=
1
2
⇒
θ
=
π
3
[
∵
cos
π
3
=
1
2
]
© examsnet.com
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